Find the radius of a circle in which a sector with central angle 45° has area 154 cm2. \(\left(\text{Use } \pi=\displaystyle\frac{22}{7}\right)\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(14\sqrt{2}\) cm
A sector with central angle \(\theta\) is the fraction \(\displaystyle\frac{\theta}{360^\circ}\) of the whole circle, so its area is \(\displaystyle\frac{\theta}{360^\circ}\times\pi r^2\).
With \(\theta=45^\circ\) and area 154 cm2: \(\displaystyle\frac{45}{360}\times\frac{22}{7}\times r^2=154\)
\(\displaystyle r^2=154\times8\times\frac{7}{22}=392\)
\(r=\sqrt{392}=\sqrt{196\times2}=\) \(14\sqrt{2}\) cm